The density of air near the Earth's surface is 1.29 kg/m^3. A helium balloon with mass of 1 kg floats in air without rising or falling . What is the minimum volume of helium in the balloon assuming the mass of the material making up the balloon is negligible .

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Near the surface of the Earth the density of air is 1.29 kg/m^3. If the mass of the material making up the balloon is negligible, it will rise upwards when the density of the gas filled in the balloon is less than 1.29 kg/m^3 and descend when the density of gas is greater than 1.29 kg/m^3.

In the question, the helium balloon neither rises up nor falls down. This gives the density of the gas in the balloon equal to exactly 1.29 kg/m^2. The minimum volume of the balloon if the mass of helium in it is 1 kg is equal to 1/1.29 = 0.7751 m^3.

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